{"paper":{"title":"$L^p$-boundedness of Berezin transforms on generalized Hartogs triangles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Qian Fu","submitted_at":"2026-06-01T15:11:59Z","abstract_excerpt":"Let $m,l\\in\\N$ be relatively prime and let \\[ \\Omega_{m/l}^{n+1}=\\bigl\\{(z,w)\\in\\C^n\\times\\C:\\ \\norm{z}^{m}<\\abs{w}^{l}<1\\bigr\\} \\] be the rational generalized Hartogs triangle of exponent $m/l$ in $\\C^{n+1}$. In this paper, we study the Berezin transform $\\BB_{m/l,n}$ associated with the Bergman kernel of $\\Omega_{m/l}^{n+1}$, and prove that $\\BB_{m/l,n}$ is bounded on $L^p(\\Omega_{m/l}^{n+1})$ if and only if $p>m+nl$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02364","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.02364/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}